I've been taught that ～くて is used when linking adjectives, but as I was reading I ran into this sentence :
What is exactly the meaning of ～くて in this sentence ? Why isn't it simply じゃない ?
There are two things that play into this
You can think of it as some sort of ellipsis (omission):
じゃない？ is often used to make a positive statement
literally Is that not a lie?
actual meaning That's a lie. / That's not true.
So (2) would be a stronger statement than (1). In particular, saying (2) makes you sound you believe the statement to be false whereas saying (1) you are simply wondering whether it could really be true.